Remark 3.3 The requirement that functions \( G_{k} \)  are uniformly bounded can be replaced by the existence
of all moments of \( G_{k}(X_{k}),\, k=1,\ldots ,K-1, \)  under \( \operatorname{P}. \)  In this case on can reformulate Theorem REF  using
generalized entropy with bracketing instead of usual entropy with bracketing (see Chapter 5.4 in [1]}).

